Обратное рассеяние электронов средних энергий в твердых телах и их влияние на процессы индуцированного осаждения углеводородов тема диссертации и автореферата по ВАК РФ 00.00.00, кандидат наук Ложкин Максим Сергеевич

• Ложкин Максим Сергеевич
• кандидат наук
• 2023

Оглавление диссертации кандидат наук Ложкин Максим Сергеевич

Введение

Глава 1. Литературный обзор

1.1 Методы растровой электронной микроскопии

1.1.1 Область взаимодействия и информационная глубина

1.1.2 Проникновение электронного пучка в твёрдое тело

1.1.3 Обратное рассеяние электронов (ОРЭ) и вторичная электронная эмиссия (ВЭ)

1.2 Методики послойного анализа образцов

1.2.1 Анализ структуры образца при помощи рентгеновского излучения

1.2.2 Методы анализа многослойных образцов при помощи рассеяных электронов

Глава 2. Экспериментальные методы

2.1 Описание экспериментальной установки

2.2 Выращивание углеродных нано- и микроструктур при облучении неподвижным электронным пучком

2.3 Приготовление многослойных образцов

2.4 Получение поперечных срезов

Глава 3. Теоретические методы исследования

3.1 Выбор дифференциальных сечений упругого и неупругого рассеяния

3.1.1 Модели упругого рассеяния электронов

3.1.2 Неупругие столкновения и потери энергии

3.2 Программный продукт для моделирования электронного

рассеяния в твёрдом теле Electron Scattering.BSE

Глава 4. Результаты и их обсуждение

4.1 Исследование механизма формирования углеродных микро- и наноструктур при непрерывном облучении неподвижным электронным пучком

4.1.1 Осаждение наностолбиков в режиме, ограниченном скоростью реакций

4.1.2 Осаждение микроколец в режиме, ограниченном переносом массы

4.2 Исследование зависимости размера области эмиссии ОРЭ от толшцны и состава слоёв в многослойных структурах

4.2.1 Двухслойные структуры

4.2.2 Структуры, содержащие более двух слоёв

4.2.3 Перспективы нанотомографии

4.3 Сравнение полученных результатов с результатами, основанными

на измерении тока ОРЭ

Заключение

Список сокращений и условных обозначений

Список литературы

Введение диссертации (часть автореферата) на тему «Обратное рассеяние электронов средних энергий в твердых телах и их влияние на процессы индуцированного осаждения углеводородов»

Введение

Исследование структуры, состава и физических свойств поверхности и расположенных на малой глубине слоёв твёрдых тел представляет принципиальный интерес для многих разделов физики и техники. Эта задача решается различными методами. Среди них одно из центральных мест принадлежит методам, использующим облучение образцов пучком ускоренных электронов. Облучение сопровождается эмиссией электронов и фотонов с различной энергией, детектирование которых даёт разнообразную информацию [1]. В потоке частиц, выходящих с поверхности массивного образца, присутствуют обратнорассеян-ные электроны (ОРЭ). Таковыми являются электроны, которые после одного или нескольких актов рассеяния на большие углы изменили направление движения на противоположное и покинули образец. Энергия ОРЭ лежит в диапазоне от исходной энергии Е0 до 50 эВ. Нижняя граница условно отделяет ОРЭ от вторичных электронов (ВЭ). Пучок рассеянных электронов заполняет область, которую называют «объем взаимодействия». Протяжённость этой области вдоль оси пучка совпадает с длиной пробега электронов. Максимальная глубина гт выхода ОРЭ меньше длины пробега, так как достигшие этой глубины электроны должны сохранить значительную часть исходной энергии, чтобы вернуться к поверхности. Ширина пучка ОРЭ определяется максимальным расстоянием гт от точки падения первичного пучка до точек пересечения траекторий ОРЭ с поверхностью образца. Величина отношения — определяет форму области эмиссии ОРЭ.

Интенсивность потока ОРЭ с поверхности неоднородного образца, состоящего из двух или более слоёв различных материалов, зависит от состава, толщины и взаимного расположения дискретных слоёв. Эта зависимость позволяет использовать измерения коэффициента обратного рассеяния для решения важной практической задачи - определения толщины покрытий, нанесённых на массивную подложку. Состав и толщина приповерхностных слоёв образца влияют не только на ток ОРЭ, но и на форму и протяжённость области эмиссии, причём значительно сильнее, чем на ток. В связи с этим кажется возможным облегчить расшифровку информации, заменяя (или дополняя) традиционные измерения тока ОРЭ измерениями линейных размеров области эмиссии. На первый

взгляд, определить протяжённость области эмиссии ОРЭ многократно сложнее, чем измерить их ток. Известно лишь немного работ по определению формы пучка электронов, рассеянных в газах или в твёрдых телах [2—4]. Трудноразрешимой проблемой является экспериментальное определение глубины эмиссии ОРЭ. В то же время измерение характерной величины латерального распространения ОРЭ не встречает принципиальных затруднений. С этой целью на образец наносят плёнку резиста и определяют смещение границы засвеченного и проявленного резиста при последовательном увеличении тока луча [5—7]. Такие измерения позволяют оптимизировать программу развёртки луча при обработке образцов методом электронной литографии. Недавно была предложена методика измерения радиального распределения ОРЭ, свободная от перечисленных недостатков [8]. Основная идея состоит в замене резиста слоем адсорбированных углеводородов, молекулы которых, как и молекулы резиста, испытывают радиа-ционно-химические превращения. Адсорбированные углеводороды присутствуют на поверхности всех образцов, помещённых в камеру РЭМ при типичном давлении остаточных газов 10-6 — 10-7 Торр. При облучении образца сфокусированным пучком электронов молекулы диффундируют к точке падения пучка и, попадая в зону эмиссии ОРЭ, распадаются, что приводит в конечном итоге к образованию кольцеобразного слоя аморфного углерода. Диаметр углеродного кольца зависит от локальной плотности тока и может служить мерой ширины гт латерального распространения ОРЭ. Глубину эмиссии гт при необходимости можно найти, используя результаты моделирования или полуэмпирические аналитические соотношения, связывающие гт с гт .

Таким образом, измерение пространственного распределения ОРЭ позволяет проверить корректность различных моделей рассеяния электронов и является промежуточным этапом на пути к анализу глубинной структуры образца.

Целью диссертационной работы является выяснение особенностей обратного рассеяния электронов, которые могут быть использованы для изучения внутреннего состава твёрдых тел, в частности, неоднородных по своему составу.

Для достижения этой цели потребовалось решить следующие задачи.

1. Разработка методов исследования латерального распределения ОРЭ, сочетающих прямые измерения с моделированием электронных траекторий методом Монте-Карло, и их применение к неоднородным по глубине образцам.

2. Сопоставление оценок размера и формы облака ОРЭ в неоднородных образцах, полученных при использовании различных моделей рассеяния, и обоснование выбора оптимальной модели рассеяния пучка ускоренных электронов в твёрдом теле.

3. Экспериментальное исследование закономерностей формирования углеродных микро- и наноструктур на поверхностях, облучаемых сфокусированным пучком электронов.

4. Поиск корреляции между диаметром углеродных микроколец и распределением по глубине дискретных слоёв образца, отличающихся по элементному составу и плотности материалов.

5. Оценка относительного вклада вторичных электронов в расширение эффективной зоны радиационного воздействия нанометрового пучка электронов.

Научная новизна:

Впервые определены размер и форма облака ОРЭ в неоднородных образцах посредством прямых измерений диаметра углеродных микроколец в сочетании с моделированием электронных траекторий методом Монте-Карло.

Впервые получены аналитические зависимости протяжённости латерального распространения ОРЭ от толщины покрытий, нанесённых на массивные подложки. Показано, что вид зависимости определяется соотношением плотности материалов подложки и поверхностного слоя.

Впервые отмечено совпадение максимальной длины траекторий ОРЭ, рассчитанной на основе модели диффузного рассеяния из точечного источника, с максимальной длиной пробега электронов, измеренной в экспериментах по пропусканию электронного пучка через тонкие плёнки.

Впервые выявлен линейный характер роста глубины эмиссии ОРЭ из неоднородных образцов с увеличением усреднённой обратной плотности пересекаемых ОРЭ слоёв.

Практическая значимость работы. Предложена и апробирована методика неразрушающего контроля и измерения толщины однослойных и многослойных тонких покрытий, нанесённых на массивные подложки. Такие покрытия применяются в различных областях техники. Проведение измерений не требует предварительного изготовления серий стандартов, аттестованных другими методами.

Предложенная методика в несколько раз менее чувствительна к флуктуациям эмиссии катода, чем методики, основанные на измерении тока ОРЭ.

Mетодология и методы исследования. В работе использовался комплексный подход исследования явлений электронного рассеяния и индуцированного осаждения на поверхности неоднородных образцов, включающий в себя теоретическое исследование с применением компьютерного моделирования электронного рассеяния методом Монте-Карло и совокупность практических методов подготовки (вакуумное термическое испарение, вакуумное ионное распыление), исследования микрорельефа (сканирующая электронная микроскопия, сканирующая зондовая микроскопия) и верификации внутренней структуры (формирование поперечного среза) многослойных структур. Также проведён неразруша-ющий анализ внутренней структуры неоднородных образцов с использованием нового экспериментального метода, основанного на явлении индуцированного электронным пучком осаждения углеводородов.

Основные положения, выносимые на защиту:

1. Метод индуцированного осаждения прекурсора сфокусированным пучком электронов средних энергий позволяет реализовать целенаправленное формирование кольцевых наноструктур на поверхности.

2. Модель индуцированного осаждения, связывающая диффузионный поток молекул углеводородов с удалённой от центра частью латерального распределения плотности тока обратнорассеянных электронов, объясняет изменение размера кольцевых структур в зависимости от параметров пучка первичных электронов.

3. Плотность твёрдого тела является основной физической характеристикой, определяющей форму и протяжённость облака обратнорассеянных электронов на его поверхности.

4. Характер зависимости размера микрокольца от толщины слоя, нанесённого на массивную подложку, определяется соотношением плотностей материалов слоя и подложки. Размер кольца монотонно растет, когда плотность материала слоя меньше плотности подложки, и линейно падает в обратном случае.

Достоверность результатов компьютерного моделирования процессов электронного рассеяния в твёрдом теле подтверждается их соответствием пред-

сказаниям теоретических моделей и результатам моделирования, полученных другими авторами для типовых образцов.

Достоверность измерений размеров углеродных микроколец обеспечивается их воспроизводимостью для образцов одинакового состава, а также достаточным объёмом накопленного материала.

Достоверность результатов измерения толщин слоёв многослойных структур подтверждается их соответствием результатам измерений, проведённых на поперечных срезах неоднородных образцов с использованием современного высокоточного оборудования Zeiss CrossBeam 1540ХВ.

Установленная зависимость максимальной длины траекторий обратнорас-сеянных электронов от плотности и элементного состава образцов согласуется с широко используемыми в литературе полуэмпирическими соотношениями, полученными при анализе прохождения ускоренных электронов через тонкие плёнки.

Апробация работы. Основные результаты работы докладывались на следующих конференциях и семинарах:

1. Жданов Г.С., Ложкин М.С. Новый подход к глубинному зондированию многослойных структур в РЭМ //В кн.: Современные методы электронной и зондовой микроскопии в исследованиях наноструктур и нано-материалов: тез. докл. 25-й Российской конференции по электронной микроскопии, т.1 — Черноголовка, 2014. — Черноголовка, изд-во Черноголовка, 2014.

2. Transient stage of nanopillar growth by focused electron beam induced deposition of carbon / Manukhova A.D., Lozhkin M.S., Zhdanov G.S.// В кн.: The 4th International Scientific Conference «State-of-the-art Trends of Scientific Research of Artificial and Natural Nanoobjects» : тез. докл. конф. — СПб, 2014. — СПб, изд-во СПбГУ, 2014

3. Dynamics of carbon nanopillar growth on bulk and thin substrates irradiated by a focused electron beam / Zhdanov G.S., Manukhova A.D., Lozhkin M.S. // в кн.: Nanotech 2014 Vol.1 «Nanotechnology 2014: Graphene, CNTs, Particles, Films & Composites» : тез. докл. конф. - 2014

4. Жданов Г.С., Ложкин М.С. Визуализация подповерхностных наноструктур в РЭМ и определение их положения в глубине образца //В кн.: XIX Российский симпозиум по растровой электронной микроскопии и ана-

литическим методам исследования твердых тел: тез. докл. конф. — Черноголовка, 2015. — Черноголовка, изд-во Черноголовка, 2015.

5. Reconstruction of a focused e-beam profile in amorphous carbon using diffusion of n-alcane molecules along carbon nanopillar sidewalls / Zhdanov G.S., Lozhkin M.S. // в кн.: Intenational Conference «Diffusion fundamentals VII» : тез. докл. конф. - Черноголовка, 2017. — Черноголовка, изд-во Черноголовка, 2017.

Личный вклад. Экспериментальные результаты, описывающие поведение наностолбиков на массивных подложках, получены автором совместно с Г. С. Ждановым и А. Д. Мануховой при непосредственном участии автора. Результаты, отражающие поведение наностолбиков на тонких плёнках и микроколец на массивных однородных и неоднородных образцах получены автором лично. Подготовка тонких плёнок аморфного углерода, массивных подложек и многослойных образцов методом вакуумного термического испарения Au/Si, Al/Cu, С/Pt, на которых выполнена основная часть работы, произведена лично автором. Изготовление серии многослойных образцов С/Pt методом вакуумного ионного распыления произведена В. Ю. Михайловским под руководством автора. Автор принимал активное участие в обсуждении, анализе и интерпретации экспериментальных результатов, а также подготовке публикаций по теме работы. Кроме того, лично автором было произведено компьютерное моделирование процессов электронного рассеяния и выполнены последующие расчёты для определения толщин слоёв методом электронной нанотомографии.

Публикации. Основные результаты по теме диссертации изложены в 8 печатных работах, 3 из которых изданы в журналах, включенных в систему цитирования Web of Science:

1. Controlling the Growth Dynamics of Carbon Nanotips on Substrates Irradiated by a Focused Electron Beam / G.S. Zhdanov, A.D. Manukhova, M. S. Lozhkin //Bulletin of the Russian Academy of Sciences. Physics. — 2014. — Сент. — Т. 78, вып. 9. — С. 881-885.

2. A new approach to probing the depths of multilayer structures in SEM /G.S. Zhdanov, M. S. Lozhkin // Bulletin of the Russian Academy of Sciences. Physics. — 2015. — Нояб. — Т. 79, вып. 11. — С. 1340-1344.

3. Anomalous Asymmetry of Carbon Nanopillar Growth on Both Sides of a Thin Substrate Irradiated with a Focused Electron Beam / G.S. Zhdanov,

M. S. Lozhkin, A.D. Manukhova // Journal of Surface Investigation: X-ray, Synchrotron and Neutron Technique. — 2017. — Т. 11, вып. 5. — С. 969-972.

5 работ представлены в тезисах докладов, список которых приведён в предыдущем параграфе.

Объем и структура работы. Диссертация состоит из введения, четырёх глав и заключения. Полный объём диссертации составляет 142 страницы с 53 рисунками и 6 таблицами. Список литературы содержит 114 наименований.

Глава 1. Литературный обзор 1.1 Методы растровой электронной микроскопии

Открытие электрона Томсоном (Thomson J.J.) в 1898 совместно с последующими экспериментальными исследованиями Резерфорда^иШегford Е.), позволившие создать первые структурированные модели вещества, поставили перед научным сообществом серьёзную задачу наблюдения микрообъектов. Особую роль на пути к решению этой проблемы сыграло установление волновой природы материальных тел и элементарных частиц, в частности, электронов, произведённое де Бройлем (deBroglie L.) в 1927 году. Это открыло перед исследователями принципиальную возможность использования электронов в качестве зондирующего воздействия на образец аналогичного пучку фотонов видимого света в оптической микроскопии. Появление электронной микроскопии, без сомнения, послужило огромным толчком для развития бесчисленного числа направлений научного исследования, так или иначе связанных с наблюдением микрообъектов. Создание первых прототипов электронного микроскопа было осуществлено в 1931 году Эрнстом Руска и Максом Кноллом (Ruska Е., Knoll М.) в Германии, в 1934 - Мартоном (Marton L.) [9] в Бельгии, а в 1939 - группой учёных под руководством Верцнера В.Н. в СССР.

Первые электронные микроскопы были просвечивающего типа и, помимо множества технических сложностей, связанных с функционированием фокусирующих систем, производили сильное разрушающие воздействие на облучаемый образец, связанное, в частности, с нагревом исследуемого образца. В 1938 году фон Арденне (vonArdenne М.) [10; 11] был создан прототип первого сканирующего просвечивающего микроскопа, осуществлявшего развёртку электронного луча вдоль образца. Этот подход дал возможность распределить электронную плотность по площади сканирования, снизив тем самым степень воздействия в каждой облучаемой точке. Продолжение развития идей сканирующей (растровой) электронной микроскопии (РЭМ) было осуществлено группой учёных под руководством Зворыкина (Zworykin V.A.) [12]. Созданный ими прибор позволял достичь разрешения в 50нм, что существенно уступало предельным

возможностям активно разрабатываемых в то время просвечивающих электрон-

р» v w

ных микроскопов. В связи с этим метод сканирующем электронной микроскопии посчитали бесперспективным и соответствующие исследования прекратились. Дальнейшее развитие РЭМ тесно связано с именем Чарльза Отли (Oatley C.W.), который сформулировал тезис о том, что для решения множества задач вовсе не нужно высокое разрешение, а всю необходимую информацию об образце можно получить, работая при умеренном увеличении. Работы Отли и его учеников сыграли ключевую роль в развитии и, что особенно важно, распространении методики сканирующей электронной микроскопии. Одним из первых успешных шагов в этом направлении стало создание растрового электронного микроскопа и получение первых изображений псевдатрёхмерного рельефа поверхности, сформированных из сигнала низкоэнергетичных вторичных электронов [13] одним из учеников Отли, МакМулланом(МcMullan D.). Отдельного упоминания заслуживает работа по созданию более совершенного детектора вторичных электронов, произведённая ещё двумя учениками Отли, Эверхартом (Everhart Т.Е.) и Торнли(Тhornley R.F.M.) [14]. Замена электронного умножителя комбинацией сцинтиллятора и фотоумножителя при детектировании электронов позволила им существенно улучшить соотношение сигнал-шум и повысить величину исходного сигнала. Достигнутый прогресс позволил уверенно заявить о том, что растровая электронная микроскопия представляет собой конкурентноспособную методику, обладающую неоспоримыми достоинствами: лёгкостью в приготовлении образцов, высокой глубиной резкости, наглядностью и простотой расшифровки получаемых снимков, а также гибкостью в отношении размеров и типов исследуемых образцов.

С момента появления первых электронных микроскопов одним из побочных явлений наблюдения образцов являлось осаждение, индуцированное электронами, впервые замеченное Стюартом (Stewart R.L.) в 1934 [15]. Появление осадка на поверхности образцов при электронном облучении рассматривалось исключительно как негативный фактор. Природа его возникновения была определена Энносом (Ennos АЕ.)[16], установившим преимущественно углеродный состав осадка. Предложенный им механизм формирования загрязнения состоит в адсорбции углеводородов, присутствующих в составе атмосферы остаточных газов вакуумной камеры, на поверхности образца. Воздействие электронов на эти адсорбированные молекулы приводит к образованию наблюдаемой

экспериментально углеродной плёнки. Для борьбы с углеродным загрязнением применялись разнообразные методы, включающие охлаждение внутренних частей вакуумной камеры для предупреждения конденсации углеводородов на образце, а также применение безмасляных (преимущественно, ртутных) насосов для вакуумных систем. Лишь в 1960 Кристи (Christу R.W.) [17] показал возможность использования индуцированного осаждения для контролируемого создания микрорельефа на поверхности образца путём её облучения электронным пучком в присутствии паров элементоорганических соединений. Эта идея легла в основу методики, известной как осаждение, индуцированное электронным пучком (ЕIectron Beam — Induced Deposition(EBID)). В настоящее время активно изучаются процессы, лежащие в основе данного способа изменения микрорельефа поверхности [18; 19]. Методика EBID предполагает применение различных прекурсоров для создания наноструктур заданного химического состава. В то же время, присутствующие в камере любого серийного РЭМ молекулы углеводородов вполне могут использоваться в качестве прекурсора для осаждения углеродных без необходимости введения дополнительного источника материала. В данной работе предлагается оригинальный метод регистрации пространственного (радиального) распределения плотности тока обратнорассе-янных электронов при помощи индуцированного осаждения углеводородов. Он позволяет судить о внутренней структуре неоднородных образцов по форме углеродного осадка, формирующегося на поверхности при облучении. Применение метода требует понимания основных процессов, связанных с рассеянием электронного пучка в твёрдом теле, о которых далее и пойдёт речь.

1.1.1 Область взаимодействия и информационная глубина

Появление области взаимодействия связано с поведением падающего электронного пучка, проникающего через поверхность вглубь образца. В процессе движения происходит взаимодействие потока падающих электронов с образцом. Часть этих электронов может быть рассеяна атомами кристаллической решётки или электронами вещества. В результате рассеяния на тяжёлых атомах движущиеся электроны отклоняются от своего первоначального направления. Это приво-

дит к расширению и перераспределению плотности в изначально сфокусированном направленном потоке электронов. Взаимодействию первичных электронов с электронами вещества, в свою очередь, сопутствует передача энергии и импульса. Первичный электрон замедляется, а переданная энергия может расходоваться на генерацию вторичных продуктов облучения. Совокупность упомянутых процессов взаимодействия с веществом приводит к формированию распределения электронной плотности вдоль направления движения падающего пучка. Объём, ограничивающий это распределение, называется областью взаимодействия.

Представление о размерах и форме области взаимодействия имеет большое значение для методик анализа, связанных с применением зондирующего электронного облучения образца. Бурное развитие подобных методик послужило толчком для ряда экспериментальных и теоретических изысканий на эту тему.

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Рисунок 1.1 — Фотографии полистирола, полученные при облучении пучком электронов с энергией от 10 кэВ до 80 кэВ. Данные из [20]

Одним из традиционных методов исследования объёма взаимодействия является наблюдение люминесценции, возникающей при облучении фосфоритов сфокусированным электронным пучком. Этот метод наиболее успешно применялся группой учёных под руководством Эренберга (Ehrenberg W.) в 1950-х [20; 21]. Излучение, возникающее вдоль всей траектории движения электрона в образце, является следствием неупругого рассеяния первичных электронов и связанного с ним возбуждения атомов вещества. Излучательная релаксация возникающих возбуждённых состояний отражает путь электрона в веществе и может быть зафиксирована фотокамерой. Примеры фотографий, отражающих результаты наблюдения люминесценции при облучении полистирола сфокусированным пучком электронов с энергией от 10 кэВ до 80кэВ, представлены на Рис. 1.1.

В начале 1970-х Брюер (Brewer G.R.)[22], а годом позже - группа учёных при участии Эверхарта (Everhart Т.Е.) [23], использовали для наблюдения области взаимодействия электронные резисты. Для электронного резиста, например, полиметилметакрилата (ПММА), характерно изменение растворимости в зависимости от дозы электронного облучения. Химическое травление ПМ-МА после экспозиции сфокусированным электронным пучком приводит к появлению полости в слое резиста. Результаты травления (Рис.1.2), представлены серией снимков профиля ПММА при одинаковом времени экспонирования электронным пучком с начальной энергией 20кэВ, но различном времени воздействия травителя. Используя известное свойство резиста, заключающееся в том, что быстрее всего растворяются те области, которые наиболее подвержены воздействию электронов, была получена зависимость формы поперечного среза объёма взаимодействия от значения плотности тока.

Изображения, соответствующие начальным этапам травления (Рис.1.2а — с), представляют собой цилиндрические полости, расположенные непосредственно под точкой падения электронного пучка. Однако при увеличении времени травления (Рис.1.2 d — f) в процесс вовлекаются участки ПММА, которые меньше повреждены электронами, что приводит не только к увеличению, но и к изменению формы области взаимодействия вплоть до грушевидной (Рис.1.2 д). Диаметр пятна сфокусированного электронного пучка в эксперименте составлял около 1мкм, а результирующие размеры области взаимодействия в каждом из направлений составляют несколько микрометров.

Рисунок 1.2 — Снимки поперечного среза протравленного ПММА после электронного облучения пучком с начальной энергией 20 кэВ с различной

дозой экспонирования [23]

Дальнейшее развитие представлений об области взаимодействия связано с развитием компьютерного моделирования электронного рассеяния методом Монте-Карло. Обсуждению возможностей применения этого метода исследования посвящена следующая глава данной работы.

1.1.2 Проникновение электронного пучка в твёрдое тело

Изучение проникновения и распространения электронного пучка является исключительно важной задачей. С точки зрения практического использования электронной микроскопии, оценка фактического разрешения методик анализа как поверхностных, так и внутренних свойств образца, опирается на форму образующегося в процессе распространения электронного потока объёма взаимодействия.

Размер и форма области взаимодействия определяются поведением электронного пучка при попадании в подповерхностные слои вещества. Характер движения ускоренных электронов внутри твёрдого тела меняется по мере увеличения глубины проникновения. При прохождении через вещество электрон претерпевает множество актов рассеяния, которые отклоняют его от начального направления, а также приводят к потерям энергии. Многократные электронные соударения меняют характер распространения электронного пучка в образце. Число актов упругого рассеяния является удобной характеристикой для обозначения границ этапов распространения электронов в образце. Можно выделить три основных этапа, последовательно сменяющих друг друга по мере увеличения глубины проникновения электронов. Начальный этап «однократного» (plural) рассеяния сменяется «многократным» (multiple) рассеянием после 20 — 30 соударений. Согласно теории, предложенной Бозе в 1929 (Bothe W.) [24], в режиме многократного рассеяния угловое распределение прошедших через слой вещества электронов описывается двумерной функцией Гаусса. В этом случае часть пучка, рассеянная в единицу телесного угла в направлении в, задаётся уравнением

Список литературы диссертационного исследования кандидат наук Ложкин Максим Сергеевич, 2023 год

Список литературы

1. Scanning Electron Microscopy and X-Ray Microanalysis. / Goldstein J. [и др.]. - 2003.

2. Cohn A., Caledonia G. Spatial Distribution of the Fluorescent Radiation Emission Caused by an Electron Beam // Journal of Applied Physics. — 1970.

3. Oelgaet G., Werner U. Kilovolt Electron Energy Loss Distribution in GaAsP // Physica status solidi (a). — 1984.

4. Experimental and theoretical study of energy dissipation profiles of keV electrons in polymethylmethacrylate / Shimizu R. [и др.] // Journal of Applied Physics. — 1975.

5. Rishton S., Kern D. Point exposure distribution measurements for proximity correction in electron beam lithography on a sub100 nm scale // Journal of Vacuum Science Technology. — 1987.

6. Raghunathan A., Hartley J. Influence of secondary electrons in high-energy electron beam lithography // Journal of Vacuum Science and Technology B. — 2013.

7. Czaplewski D., Ocola L. Variation of backscatter electron intensity // Journal of Vacuum Science and Technology B. — 2013.

8. Способ томографического анализа образца в растровом электронном микроскопе : 2453946 / Жданов Г. — заявл. 2012.

9. Marton L. Electron Microscopy of Biological Objects // Nature. — 1934.

10. Ardenne M. von. Das Elektronen-Rastermikroskop. Theoretische Grundlagen // Zeitschrift für Physik. — 1938.

11. Ardenne M. von. Das Elektronen-Rastermikroskop. Praktische Ausfuhrung. // Zeitschrift fur technische Physik. — 1938.

12. Zworykin V. A., Hillier J., L. S. R. A scanning electron microscope // ASTM Bulletin. — 1942.

13. McMullan D. An improved scanning electron microscope for opaque specimens. // Proceedings of the Institute of Electrical and Electronics Engineers. — 1953.

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

Everhart T. E., Thornley R. F. M. Wide-band detector for micro-microampere low-energy electron currents. // Journal of Scientific Instruments. — 1960.

Stewart R. L. Insulating Films Formed Under Electron and Ion Bombardment // Physical Review. — 1934.

Ennos A. The origin of specimen contamination in the electron microscope // British Journal of Applied Physics. — 1953.

Christy R. W. Formation of Thin Polymer Films by Electron Bombardment // Journal of Applied Physics. — 1960.

Dorp W. F. van, Hagen C. W. A critical literature review of focused electron beam induced deposition // Journal of Applied Physics. — 2008.

Electron-Beam-Induced Deposition as a Technique for Analysis of Precursor Molecule Diffusion Barriers and Prefactors / Cullen J. [h gp.] // ACS Applied Materials and Interfaces. — 2015.

Ehrenberg W., King D. The Penetration of Electrons into Luminescent Materials // Proceedings of the Physical Society. — 1963.

Ehrenberg W., Franks J. The Penetration of Electrons into Luminescent Material // Proceedings of the Physical Society. Section B. — 1953.

Brewer G. The application of electron/ion beam technology to microelectronics // IEEE spectrum. — 1971.

Computer-Controlled Resist Exposure in the Scanning Electron Microscope / Herzog R. F. [h gp.] // IEEE Transactions on Electron Devices. — 1972.

Bothe W. Die Streuabsorption der Electronenstrahlen // Zeitschrift fur Physik. — 1929.

Cosslett V., Thomas R. The plural scattering of 20 kev electrons // British Journal of Applied Physics. — 1964.

Cosslett V. E., Thomas R. N. Multiple scattering of 5-30 kev electrons in evaporated metal films I. Total transmission and angular distribution // British Journal of Applied Physics. — 1964.

Archard G. Back Scattering of Electrons // Journal of Applied Physics. — 1961.

Kanaya K., Okayama S. Penetration and energy-loss theory of electrons in solid targets // Journal of Applied Physics. — 1972.

29. Rau E., Robinson V. An Annular Toroidal Backscattered Electron Energy Analyser for Use in Scanning Electron Microscopy // Scanning. — 1996.

30. Schlichting F., Berger D., Niedrig H. Thickness Determination of Ultra-Thin Films Using Backscattered Electron Spectra of a New Toroidal Electrostatic Spectrometer // Scanning. — 1999.

31. Cosslett V., Thomas R. Multiple scattering of 5-30 keV electrons in evaporated metal films II: Range-energy relations // British Journal of Applied Physics. — 1964.

32. Cosslett V., Thomas R. Multiple scattering of 5 - 30 keV electrons in evaporated metal films III: Backscattering and absorption // British Journal of Applied Physics. — 1965.

33. Sim K., White J. New technique for in-situ measurement of backscattered and secondary electron yields for the calculation of signal-to-noise ratio in a SEM // Journal of Microscopy. — 2005.

34. Bishop H. title // Proceedings of the 4th International Conference on X-ray Optics and Microanalysis / под ред. Castaing R., Deschamps P., Philibert J. — 1966.

35. Heinrich K. F. J. title // Proceedings of the 4th International Conference on X-ray Optics and Microanalysis / под ред. Castaing R., Deschamps P., Philibert J. — 1966.

36. Shimizu R., Ding Z.-J.Monte Carlo modelling of electron-solid interactions // Reports on Progress in Physics. — 1992.

37. Herrmann R., Reimer L. Backscattering coefficient of multicomponent specimens // Scanning. — 1984.

38. Seah M., Dench W. Quantitative Electron Spectroscopy of Surfaces: A Standart Data Base for Electron Inelastic Mean Free Paths in Solids // Surface and Interface Analysis. — 1979.

39. Seiler H. Secondary electron emission in the scanning electron microscope // Journal of Applied Physics. — 1960.

40. Elliott S., Broom R., Humphreys C. Dopant profiling with the scanning electron microscope - A study of Si // Journal of Applied Physics. — 2002.

41

42

43

44

45

46

47

48

49

50

51

52

53

Analytical electron microscopy and Auger electron spectroscopy study of low-temperature diffusion in multilayer chromium-copper-nickel-gold thin films / Danylenko M. [h gp.] // Thin Solid Films. — 2003.

Bishop H. E., Poole D. M. A simple method of thin film analysis in the electron probe microanalyser // Journal of Physics D: Applied Physics. — 1973.

Accuracy of Film Thickness Determination in Electron Probe Microanalysis / Moller A. [h gp.] // Mikrochimica Arta. — 1995.

EDX depth profiling by means of effective layers / Myint K. [h gp.] // Fresenius' Journal of Analytical Chemistry. — 1998.

Sempf K., Herrmann M., Bauer F. First results in thin film analysis based on a new EDS software to determine composition and/or thickness of thin layers on substrates // EMC 2008 14th European Microscopy Congress 1-5 September 2008, Aachen, Germany, Volume 1: Instrumentation and Methods / nog peg. Luysberg M., Tillmann K., Weirich T. — 2008.

Metallic thin film depth measurements by X-ray microanalysis / Ng F. [h gp.] // Applied Surface Science. — 2006.

Canli S. Thickness Ananlysis of Thin Films by Energy Dispersive X-ray Spectroscopy : type / Canli S. — Middle East Technical University, 2010.

Film Thickness Measurements of SiO2 by XPS / Mitchell D. [h gp.] // Surface and Interface Analysis. — 1994.

Geneg S., Zhang S., Onishi H. Precision Thickness Measurement of Ultra-Thin Films via XPS // Material Science Forum. — 2003.

Kim K. J., Park K. T., Lee J. W. Thickness measurement of SiO2 films thinner than 1 nm by X-ray photoelectron spectroscopy // Thin Solid Films. — 2006.

Holloway P. Thickness determination of ultrathin films by Auger electron spectroscopy // Journal of Vacuum Science and Technology. — 1975.

Auger Electron Spectroscopy: A Rational Method for Determining Thickness of Graphene Films / Xu M. [h gp.] // ACS Nano. — 2010.

Sutter P, Sutter E. Thickness determination of few-layer hexagonal boron nitride films by scanning electron microscopy and Auger electron spectroscopy // APL Materials. — 2014.

54. Haimovich J., Leibold K., Staudt G. Estimating and Measuring Thickness of Thin Layers by Monte Carlo Simulation and Backscattered Electron Image Analysis // AMP Journal of Technology. — 1996.

55. Dremova N., Yakimov E. SEM characterization of multilayer structures // Vacuum. — 1991.

56. Joy D. C. Monte Carlo Modeling For Electron Microscopy And Microanalysis. — 1995.

57. Improvements to the design of an electrostatic toroidal backscattered electron spectrometer for the scanning electron microscope / Rau E. [и др.] // Review of Scientific Instruments. — 2002.

58. Niedrig H., Rau E. Information depth and spatial resolution in BSE microtomography in SEM // Nuclear Instruments and Methods in Physics Research B. — 1998.

59. Усовершенствование электронного тороидального спектрометра для растрового электронного микроскопа и его новые применения в диагностике структур микро- и наноэлектроники / Рау Э. [и др.] // Журнал технической физики. — 2013.

60. Comparison of experimental and Monte Carlo simulated BSE spectra of multilayered structures and "in-depth"measurements in a SEM / Rau E. [и др.] // Journal of Physics D: Applied Physics. — 2002.

61. Zhenyu T., Yueyuan X. A Monte Carlo Study of the Thickness Determination of Ultra-Thin Films // Scanning. — 2002.

62. Brewer A., Dibeler V. Mass spectrometric analyses of hydrocarbon and gas mixtures // Journal of Research of the National Bureau of Standards. — 1945.

63. Wolff R., Wolff G., McCloskey J.Characterization of unsaturated hydrocarbons by mass spectrometry // Tetrahedron. — 1966.

64. CASINO V2.42 — A Fast and Easy-to-use Modeling Tool for Scanning Electron Microscopy and Microanalysis Users / Drouin D. [и др.] // Scanning. — 2007.

65. Wentzel G. Zwei Bemerkungen über die Zerstreuung korpuskularer Strahlen als Beugungserscheinung // Zeitschrift fur Physik. — 1926.

66. Murata K. Spatial distribution of backscattered electrons on the scanning electron microscope and electron microprobe // Journal of Applied Physics. — 1974.

67. A Monte Carlo approach to the direct simulation of electron penetration in solids / Shimizu R. [h gp.] // Journal of Physics D: Applied Physics. — 1976.

68. Yoshikawa H., Shimizu R., Ding Z.-J. On the radial distribution function for sub-kV backscattered electron diffraction from a disordered surface // Surface Science. — 1991.

69. Bunyan P. J., Schonfelder J. L. Polarization by mercury of 100 to 2000 eV electrons // Proceedings of the Physical Society. — 1965.

70. Riley M. E., MacCallum C. J., Biggs F. Theoretical Electron-Atom Elastic Scattering Cross Sections: Selected Elements, 1 keV to 256 keV // Atomic Data and Nuclear Data Tables. — 1975.

71. Ichimura S., Shimizu R. Backscattering correction for quantitative Auger analysis // Surface Science. — 1981.

72. Reimer L., Krefting E. Use of Monte Carlo Calculations in Electron Probe Microanalysis and Scanning Electron Microscopy // National Bureau of Standarts. — 1976.

73. Gauvin R., Drouin D. A Formula to Compute Total Elastic Mott Cross-Sections // Scanning. — 1993.

74. Low-Energy Electron/Atom Elastic Scattering Cross Sections from 0.1-30 keV / Browning R. [h gp.] // Scanning. — 1995.

75. Reimer L., Lodding B. Calculation and Tabulation of Mott Cross-Sections for Large-Angle Electron Scattering // Scanning. — 1984.

76. Calculations of Mott scattering cross section / Czyzewski Z. [h gp.] // Journal of Applied Physics. — 1990.

77. Salvat F., Jablonski A., Powell C. ELSEPA—Dirac partial-wave calculation of elastic scattering of electrons and positrons by atoms, positive ions and molecules // Computer Physics Communications. — 2005.

78. Reimer L. Scanning Electron Microscopy: Physics of Image Formation and Microanalysis. — 1985.

79. Tables of energy losses and ranges of electrons and positrons. — 1964.

80. Rao-Sahib T., Wittry D. X-ray continuum from thick elemental targets for 10-50 keV electrons // Journal of Applied Physics. — 1974.

81. Love G., Cox M., Scott V. A versatile atomic number correction for electron-probe microanalysis // Journal of Physics D: Applied Physics. — 1978.

82. Zhenyu T., Yancai H. An Empirical Energy Loss Equation of Electrons // Scanning. — 2002.

83. Luo S., Joy D. An empirical stopping power relationship for low-energy electrons // Scanning. — 1989.

84. Green A., Leckey R. Scattering of 2-20 KeV electrons in aluminium // Journal of Physics D: Applied Physics. — 1976.

85. Ding Z.-J., Shimizu R. A Monte Carlo Modeling of Electron Interaction with Solids Including Cascade Secondary Electron Production // Scanning. — 1996.

86. Gryzinski M. Classical Theory of Electronic and Ionic Inelastic Collisions // Physical Review. — 1959.

87. Quinn J., Ferrell R. Electron Self-Energy Approach to Correlation in a Degenerate Electron Gas // Physical Review. — 1958.

88. Ding Z., Tang X., Shimizu R. Monte Carlo study of secondary electron emission // Journal of Applied Physics. — 2001.

89. Lowney J.Monte Carlo Simulation of Scanning Electron Microscope Signals for Lithographic Metrology // Scanning. — 1996.

90. Powell C. Cross sections for ionization of inner-shell electrons by electrons // Reviews of Modern Physics. — 1976.

91. Penn D. Electron mean-free-path calculations using a model dielectric function // Physical Review B. — 1987.

92. Ding Z.-J., Shimizu R. Inelastic collisions of kV electrons in solids // Surface Science. — 1989.

93. Analytical and Numerical Approaches to Calculating the Escape Function for the Emission of Medium-Energy Electrons from Uniform Specimens / Bakalerenikov L. A. [h gp.] // Technical Physics. — 2001.

94. Жданов Г. О скорости углеводородного загрязнения объектов в микрозон-довых системах // Поверхность. — 1983.

95. Kinetics of Carbon Nanopillar Formation on a Pyrolytic Graphite Surface during Reactions Induced by a Focused Electron Beam / Zhdanov G. [и др.] // Bulletin of the Russian Academy of Sciences. — 2013.

96. Influence of sub-100 nm scattering on high-energy electron beam lithography / Anderson E. [и др.] // Journal of Vacuum Science and Technology B: Microelectronics and Nanometer Structures. — 2001.

97. Czaplewski D., Holt M., Ocola L. The range and intensity of backscattered electrons for use in the creation of high fidelity electron beam lithography patterns // Nanotechnology. — 2013.

98. Smith D., Fowlkes J., Rack P. A nanoscale three-dimensional Monte Carlo simulation of electron-beaminduced deposition with gas dynamics // Nanotechnology. — 2007.

99. Smith D., Fowlkes J., Rack P. Simulating the effects of surface diffusion on electron beam induced deposition via a three-dimensional Monte Carlo simulation // Nanotechnology. — 2008.

100. Hollenshead J., Klebanoff L. Modeling radiation-induced carbon contamination of extreme ultraviolet optics // Journal of Vacuum Science Technology B. — 2006.

101. Zhdanov G. S., Lozhkin M. S., Manukhova A. D. Controllig the Growth Dynamics of Carbon Nanotips on Substrates Irradiated by a Focused Electron Beam // Bulletin of the Russian Academy of Sciences: Physics. — 2014. — Vol. 78, no. 9. — P. 881-885.

102. Design High-Efficiency Si Nanopillar-Array-Textured Thin-Film Solar Cell / Wong S. M. [и др.] // IEEE Electron Device Letters. — 2010.

103. Biophysical Model of Bacterial Cell Interactions with Nanopatterned Cicada Wing Surfaces / Pogodin S. [и др.] // Biophysical Journal. — 2013.

104. Rykaczewski K., White W., Fedorov A. Analysis of electron beam induced deposition (EBID) of residual hydrocarbons in electron microscopy // Journal of Applied Physics. — 2007.

105. Liu Z.-Q., Mitsuishi K., Furuya K. A dynamic Monte Carlo study of the in situ growth of a substance deposited using electron-beam-induced deposition // Nanotechnology. — 2006.

106. Zhdanov G. S., Lozhkin M. S., Manukhova A. D. Anomalous asymmetry of carbon nanopillar growth on both sides of a thin substrate irradiated with a focused electron beam // Journal of Surface Investigation. — 2017. — No. 9. — P. 969-972.

107. Chang T. Proximity effect in electronbeam lithography // Journal of Vacuum Science and Technology. — 1975.

108. Muller K. Speed-controlled electron-microrecoder, 1 // Optik. — 1971.

109. Watson J. An Effect of Electron Bombardment upon Carbon Black // Journal of Applied Physics. — 1947.

110. Hillier J. On the Investigation of Specimen Contamination in the Electron Microscope // Journal of Applied Physics. — 1948.

111. Surface diffusion of n-alkanes on Ru(001) / Brand J. L. [h gp.] // Journal of Chemical Physics. — 1990.

112. Fichthorn K., Miron R. Thermal Desorption of Large Molecules from Solid Surfaces // Physical Review Letters. — 2002.

113. Zhdanov G. S., Lozhkin M. S. A new approach to probing the depths of multilayer structures in SEM // Bulletin of the Russian Academy of Sciences: Physics. — 2015. — Vol. 79, no. 11. — P. 1340-1344.

114. Dapor M. Monte Carlo simulation of backscattered electrons and energy from thick targets and surface films // Physical Review B. — 1992.

SAINT-PETERSBURG UNIVERSITY

Manuscript Copyright

Lozhkin Maksim Sergeevich

Backscattering of Medium-Energy Electrons in Solids and their effect on the processes of hydrocarbons induced deposition

Scientific specialty 1.3.8. Physics of Condensed Matter

Dissertation is submitted for the degree of Candidate of Physical and Mathematical

Sciences Translation from Russian

Scientific Advisor: Doctor of Physical and Mathematical Sciences Chizhov Yuri Vladimirovich

St. Petersburg — 2023

Table of contents

p.

Introduction........................................................................4

Chapter 1. Literature review......................................................10

1.1 Scanning electron microscopy methods....................................10

1.1.1 Interaction area and information depth............................12

1.1.2 Penetration of an electron beam into a solid body ................15

1.1.3 Electron backscattering (BSE) and secondary electron emission (SE)................................................................19

1.2 Methods of layer-by-layer analysis of samples ............................25

1.2.1 Analysis of sample structure using X-rays ............27

1.2.2 Methods for analyzing multilayer samples using scattered electrons ............................................................30

Chapter 2. Experimental methods........................37

2.1 Description of the experimental setup...................37

2.2 Growing of carbon nano- and microstructures under irradiation with a stationary electron beam ....................................................39

2.3 Preparation of multilayer samples.....................40

2.4 Getting cross sections ......................................................43

Chapter 3. Theoretical research methods ....................45

3.1 Choice of differential cross sections for elastic and inelastic scattering . 45

3.1.1 Models of elastic scattering of electrons.............46

3.1.2 Inelastic collisions and energy losses ..............................50

3.2 Software for modeling electron scattering in solids

Electron Scattering.BSE........................55

Chapter 4. Results and their discussion .....................65

4.1 Study of the formation mechanism of carbon micro- and nanostructures

under continuous irradiation with a stationary electron beam ............65

4.1.1 Deposition of nanopillars in the reaction rate-limited mode ... 67

4.1.2 Deposition of micro-rings in a mode limited by mass transfer . . 75

4.2 Investigation of the dependence of the size of the BSE emission region

on the thickness and composition of layers in multilayer structures . . . 104

4.2.1 Two-layer structures........................107

4.2.2 Structures containing more than two layers............119

4.2.3 Prospects for nanotomography..................120

4.3 Comparison of the obtained results with the results based on the measurement of the BSE current.....................120

Conclusion ..................................... 123

List of abbreviations and conventions......................125

Bibliography....................................126

Introduction

The study of the structure, composition and physical properties of the surface and layers of solids located at a shallow depth is of fundamental interest for many branches of physics and technology. This problem is solved by various methods. Among them, one of the central places belongs to methods that use the irradiation of samples with a beam of accelerated electrons. Irradiation is accompanied by the emission of electrons and photons with different energies, the detection of which provides a variety of information [1]. The flow of particles emerging from the surface of a massive sample contains backscattered electrons (BSE). These are electrons that, after one or several large-angle scattering events, reversed their direction of motion and left the sample. The BSE energy lies in the range from the initial energy E0 to 50 eV. The lower boundary conditionally separates the BSE from secondary electrons (SE). A beam of scattered electrons fills the region, which is called the "interaction volume". The length of this region along the beam axis coincides with the electron path length . The maximum depth zm of the BSE exit is less than the path length, since the electrons that have reached this depth must retain a significant part of the initial energy in order to return to the surface. The width of the BSE beam is determined by the maximum distance rm from the point of incidence of the primary beam to the intersection points of the BSE trajectories with the sample surface. The value of the — ratio determines the shape of the BSE emission region.

The intensity of the BSE flow from the surface of an inhomogeneous sample, consisting of two or more layers of different materials, depends on the composition, thickness, and relative position of the discrete layers. This dependence makes it possible to use measurements of the backscattering coefficient to solve an important practical problem, namely, to determine the thickness of coatings deposited on a massive substrate. The composition and thickness of the near-surface layers of the sample affect not only the BSE current, but also the shape and extent of the emission region, and much more strongly than the current. In this regard, it seems possible to facilitate the interpretation of information by replacing (or supplementing) the traditional measurements of the BSE current with measurements of the linear dimensions of the emission region. At first glance, it is much more difficult to determine the extent of the BSE emission region than to measure their current. Only a few works are known to deter-

mine the shape of an electron beam scattered in gases or solids [2-4]. An intractable problem is the experimental determination of the depth of the BSE emission. At the same time, the measurement of the characteristic value of the lateral spread of the BSE does not encounter fundamental difficulties. For this purpose, a resist film is applied to the sample and the displacement of the border of the illuminated and developed resist is determined with a successive increase in the beam current [5-7]. Such measurements make it possible to optimize the beam sweep program during sample processing by electron lithography. Recently, a method for measuring the radial distribution of the BSE, free from the above disadvantages [8], has been proposed. The main idea is to replace the resist with a layer of adsorbed hydrocarbons, whose molecules, like those of the resist, undergo radiation-chemical transformations. Adsorbed hydrocarbons are present on the surface of all samples placed in the SEM chamber at a typical residual gas pressure of 10-6 —10-7 Torr. When the sample is irradiated with a focused electron beam, the molecules diffuse to the point of incidence of the beam and, falling into the zone of emission of the BSE, decompose, which ultimately leads to the formation of an annular layer of amorphous carbon. The diameter of the carbon ring depends on the local current density and can serve as a measure of the width rm of the lateral propagation of the BSE. The emission depth zm can be found, if necessary, using simulation results or semi-empirical analytical relations relating zm to rm .

Thus, the measurement of the spatial distribution of the BSE makes it possible to check the correctness of various models of electron scattering and is an intermediate step on the way to the analysis of the deep structure of the sample.

Aim dissertation work is to elucidate the features of electron backscattering, which can be used to study the internal composition of solids, in particular, those that are inhomogeneous in composition.

To achieve this goal, it was necessary to solve the following tasks.

1. Development of methods for studying the lateral distribution of the BSE, combining direct measurements with the simulation of electron trajectories by the Monte Carlo method, and apply them to samples that are inhomogeneous in depth.

2. Comparison of estimates of the size and shape of the BSE cloud in inhomoge-neous samples, obtained using different scattering models, and substantiation of the choice of the optimal model for the scattering of a beam of accelerated electrons in a solid body.

3. Experimental study of the patterns of formation of carbon micro- and nanos-tructures on surfaces irradiated by a sharply focused electron beam.

4. Search for a correlation between the diameter of carbon microrings and the depth distribution of discrete layers of a sample that differ in elemental composition and density of materials.

5. Estimation of the relative contribution of secondary electrons to the expansion of the effective zone of radiation action of a nanometer electron beam.

Novelity:

For the first time, the size and shape of the BSE cloud in inhomogeneous samples were determined by direct measurements of the diameter of carbon microrings in combination with Monte Carlo simulation of electron trajectories.

For the first time, analytical dependences of the extent of the lateral propagation of the BSE on the thickness of coatings deposited on massive substrates have been obtained. It is shown that the type of dependence is determined by the ratio of the density of the materials of the substrate and the surface layer.

For the first time, the coincidence of the maximum length of the BSE trajectories, calculated on the basis of the model of diffuse scattering from a point source, with the maximum length of the electron path, measured in experiments on the transmission of an electron beam through thin films, was noted.

For the first time, a linear nature of the increase in the depth of the BSE emission from inhomogeneous samples with an increase in the average reciprocal density of the layers crossed by the BSE has been revealed.

Influence of study. A technique for non-destructive testing and measurement of the thickness of single-layer and multilayer thin coatings deposited on massive substrates has been proposed and tested. Such coatings are used in various fields of technology. Carrying out measurements does not require preliminary production of a series of standards certified by other methods. The proposed technique is several times less sensitive to cathode emission fluctuations than the techniques based on the measurement of the BSE current.

Methods. We used a comprehensive approach to studying the phenomena of electron scattering and induced deposition on the surface of inhomogeneous samples, which includes a theoretical study using computer simulation of electron scattering by the Monte Carlo method and a set of practical preparation methods (vacuum thermal evaporation, vacuum ion sputtering), microrelief studies ( scanning electron microscopy,

scanning probe microscopy) and verification of the internal structure (formation of a cross section) of multilayer structures. A non-destructive analysis of the internal structure of inhomogeneous samples was also carried out using a new experimental method based on the phenomenon of hydrocarbon deposition induced by an electron beam.

Basic depositions submitted for defense:

1. The method of induced deposition of a precursor by a focused medium-energy electron beam makes it possible to implement the targeted formation of ring nanostructures on the surface.

2. The model of induced deposition, which relates the diffusion flow of hydrocarbon molecules to the part of lateral distribution of the current density of backscattered electrons remote from the center, makes it possible to explain the change in size of ring structures depending on the parameters of primary electron beam.

3. The density of a solid body is the main physical characteristic that determines the shape and extent of the cloud of backscattered electrons on its surface.

4. The nature of the dependence of microring size on layer thickness for the layer deposited on the massive substrate is determined by the densities ratio of the layer materials and the substrate material. The size of the ring increases mono-tonically when the density of the layer material is less than the density of the substrate material, and decreases linearly in the opposite case.

Reliability of the results of computer simulation of the processes of electron scattering in a solid are confirmed by their compliance with the predictions of theoretical models and the simulation results obtained by other authors for standard samples.

The reliability of measurements of the dimensions of carbon microrings is ensured by their reproducibility for samples of the same composition, as well as by a sufficient amount of accumulated material.

The reliability of the results of measuring the thicknesses of layers of multilayer structures is confirmed by their agreement with the results of measurements carried out on cross sections of inhomogeneous samples using modern high-precision equipment Zeiss CrossBeam 1540XB.

The established dependence of the maximum length of the BSE trajectories on the density and elemental composition of the samples is consistent with the semi-empirical relations widely used in the literature, obtained by analyzing the passage of accelerated electrons through thin films.

Probation. The main results of the work were reported at the following conferences and seminars:

1. Zhdanov G.S., Lozhkin M.S. A new approach to deep probing of multilayer structures in SEM // In the book: Modern methods of electron and probe microscopy in the study of nanostructures and nanomaterials: abstracts. report 25th Russian Conference on Electron Microscopy, v.1 — Chernogolovka, 2014. — Chernogolovka, publishing house Chernogolovka, 2014.

2. Transient stage of nanopillar growth by focused electron beam induced deposition of carbon / Manukhova A.D., Lozhkin M.S., Zhdanov G.S.// In book: The 4th International Scientific Conference «State-of-the-art Trends of Scientific Research of Artificial and Natural Nanoobjects» :abstract report conf. — St. Petersburg, 2014. — St. Petersburg, publishing house of St. Petersburg State University, 2014

3. Dynamics of carbon nanopillar growth on bulk and thin substrates irradiated by a focused electron beam / Zhdanov G.S., Manukhova A.D., Lozhkin M.S. // in book: Nanotech 2014 Vol.1 «Nanotechnology 2014: Graphene, CNTs, Particles, Films & Composites» : abstract report conf. - 2014

4. Zhdanov G.S., Lozhkin M.S. Visualization of subsurface nanostructures in SEM and determination of their position in the depth of the sample. report conf. — Chernogolovka, 2015. — Chernogolovka, publishing house Chernogolovka, 2015.

5. Reconstruction of a focused e-beam profile in amorphous carbon using diffusion of n-alcane molecules along carbon nanopillar sidewalls / Zhdanov G.S., Lozhkin M.S. //in book: International Conference "Diffusion fundamentals VII" : abstract. report conf. - Chernogolovka, 2017. — Chernogolovka, publishing house Chernogolovka, 2017.

Author contribution. Experimental results describing the behavior of nanopil-lars on massive substrates were obtained by the author jointly with G. S. Zhdanov and A. D. Manukhova with the direct participation of the author. The results reflecting the behavior of nanopillars on thin films and microrings on massive homogeneous and inhomogeneous samples were personally obtained by the author. The preparation of thin films of amorphous carbon, massive substrates and multilayer samples by vacuum thermal evaporation of Au/Si, Al/Cu, C/Pt, on which the main part of the work was performed, was carried out personally by the author. The fabrication of a series of C/Pt

multilayer samples by vacuum ion sputtering was carried out by V. Yu. Mikhailovsky under the guidance of the author. The author took an active part in the discussion, analysis and interpretation of experimental results, as well as the preparation of publications on the topic of the work. In addition, the author personally performed computer simulation of electron scattering processes and performed subsequent calculations to determine the thickness of the layers using electron nanotomography.

Publications. The main results on the topic of the dissertation are presented in 8 publications, 3 of which were published in journals included in the Web of Science citation system:

1. Controlling the Growth Dynamics of Carbon Nanotips on Substrates Irradiated by a Focused Electron Beam / G.S. Zhdanov, A.D. Manukhova, M. S. Lozhkin //Bulletin of the Russian Academy of Sciences. Physics. — 2014. — Vol. 78, Num. 9.—p. 881-885.

2. A new approach to probing the depths of multilayer structures in SEM / G.S. Zhdanov, M. S. Lozhkin // Bulletin of the Russian Academy of Sciences. Physics. — 2015. — Vol. 79, Num. 11. — p. 1340-1344.

3. Anomalous Asymmetry of Carbon Nanopillar Growth on Both Sides of a Thin Substrate Irradiated with a Focused Electron Beam / G.S. Zhdanov, M. S. Lozhkin, A.D. Manukhova // Journal of Surface Investigation: X-ray, Synchrotron and Neutron Technique. — 2017. —Vol. 11, Num. 5. —p. 969-972.

5 studies are presented in the abstracts of reports, the list of which is given in the previous paragraph.

Scope and structure of the study. The dissertation consists of an introduction, four chapters and a conclusion. The full scope of the dissertation is 134 pages with 53 images and with 6 tables. The list of references contains 114 cites.

Chapter 1. Literature review 1.1 Scanning electron microscopy methods

The discovery of the electron by Thomson J. J. in 1898, together with subsequent experimental studies by Rutherford E., which made it possible to create the first structured models of matter, posed a serious problem for the scientific community to observe microobjects. De Broglie L. in 1927 played a special role on the way to solving this problem. This opened up to researchers the fundamental possibility of using electrons as a probing effect on a sample, similar to a beam of visible light photons in optical microscopy. The advent of electron microscopy, no doubt, served as a huge impetus for the development of countless areas of scientific research, one way or another connected with the observation of microobjects. The creation of the first electron microscope prototypes was carried out in 1931 by Ruska E. and Knoll M. in Germany, in 1934 by Marton L. [9] in Belgium, and in 1939 - by a group of scientists led by Vertsner V.N. in USSR.

The first electron microscopes were of the transmission type and, in addition to many technical difficulties associated with the operation of focusing systems, produced a strong destructive effect on the irradiated sample, associated, in particular, with heating the sample under study. In 1938 von Ardenne M. [10; 11] created a prototype of the first scanning transmission microscope that scanned an electron beam along a sample. This approach made it possible to distribute the electron density over the scanning area, thereby reducing the degree of impact at each irradiated point. The continuation of the development of the ideas of scanning (scanning) electron microscopy (SEM) was carried out by a group of scientists led by Zworykin V.A. [12]. The device they created made it possible to achieve a resolution of 50nm, which was significantly inferior to the limiting capabilities of the transmission electron microscopes actively developed at that time. In this regard, the method of scanning electron microscopy was considered unpromising and the corresponding studies were stopped. The further development of the SEM is closely related to the name of Oatley C.W., who formulated the thesis that solving many problems does not require high resolution at all, and all the necessary information about the sample can be obtained by working at moderate magnification. The

work of Otley and his students played a key role in the development and, most importantly, in the dissemination of the technique of scanning electron microscopy. One of the first successful steps in this direction was the creation of a scanning electron microscope and the acquisition of the first images of a pseudo-three-dimensional surface relief formed from a signal of low-energy secondary electrons [13] by one of Otley's students, McMullan D. Special mention deserves the work on the creation of a more advanced secondary electron detector, produced by two more students of Otley, Everhart T. E. and Thornley R. F. M. [14]. Replacing the electron multiplier with a combination of a scintillator and a photomultiplier for electron detection allowed them to significantly improve the signal-to-noise ratio and increase the magnitude of the original signal. The progress achieved has made it possible to confidently state that scanning electron microscopy is a competitive technique with undeniable advantages: ease of sample preparation, high depth of field, clarity and ease of interpretation of the resulting images, as well as flexibility in terms of the size and types of samples under study.

Since the advent of the first electron microscopes, one side effect of observing samples has been electron-induced deposition, first noticed by Stewart R.L. in 1934 [15]. The appearance of a precipitate on the surface of samples under electron irradiation was considered exclusively as a negative factor. The nature of its occurrence was determined by Ennos A. E. [16], who established the predominantly carbon composition of the sediment. The mechanism of pollution formation proposed by him consists in the adsorption of hydrocarbons, which are present in the composition of atmosphere of the residual gases of SEM vacuum chamber, on the surface of the sample. The action of electrons on these adsorbed molecules leads to the formation of an experimentally observed carbon film. A variety of methods have been used to combat carbon contamination, including cooling the interior of the vacuum chamber to prevent condensation of hydrocarbons on the sample, and the use of oil-free (predominantly mercury) pumps for vacuum systems. Only in 1960 Christy R. W. [17] showed the possibility of using induced deposition for controlled creation of a microrelief on the sample surface by irradiating it with an electron beam in the presence of vapors of organoelement compounds. This idea formed the basis of a technique known as electron beam-induced deposition (Electron Beam — Induced Deposition(EBID)). Currently, the processes underlying this method of changing the surface microrelief [18; 19] are being actively studied. The EBID technique involves the use of various precursors to create nanostructures of a given chemical composition. At the same time, hydrocarbon molecules present in the

chamber of any serial SEM can be used as a precursor for carbon deposition without the need to introduce an additional source of material. In this paper, we propose an original method for recording the spatial (radial) distribution of the current density of backscattered electrons using induced hydrocarbon deposition. It makes it possible to judge the internal structure of inhomogeneous samples from the shape of the carbon deposit formed on the surface during irradiation. The application of the method requires an understanding of the basic processes associated with the scattering of an electron beam in a solid, which will be discussed below.

1.1.1 Interaction area and information depth

The appearance of the interaction region is related to the behavior of the incident electron beam penetrating deep into the sample through the surface. In the process of motion, the flow of incident electrons interacts with the sample. Some of these electrons can be scattered by atoms of the crystal lattice or electrons of matter. As a result of scattering by heavy atoms, moving electrons deviate from their original direction. This leads to expansion and density redistribution in the initially focused directed electron flow. The interaction of primary electrons with the electrons of matter, in turn, is accompanied by the transfer of energy and momentum. The primary electron slows down, and the transferred energy can be spent on the generation of secondary irradiation products. The totality of the mentioned processes of interaction with matter leads to the formation of an electron density distribution along the direction of the incident beam. The volume that limits this distribution is called the interaction area.

The idea of the size and shape of the interaction region is of great importance for the analysis methods associated with the use of probing electron irradiation of the sample. The rapid development of such techniques served as an impetus for a number of experimental and theoretical studies on this topic.

One of the traditional methods for studying the volume of interaction is the observation of luminescence that occurs when phosphorites are irradiated with a focused electron beam. This method was most successfully used by a group of scientists led by Ehrenberg W. in the 1950s [20; 21]. The radiation that appears along the entire trajectory of the electron in the sample is a consequence of the inelastic scattering of primary

Fig. 1.1 — Photographs of polystyrene obtained by irradiation with an electron beam with energies from 10 keV to 80 keV. Data from [20]

electrons and the associated excitation of the atoms of the substance. The radiative relaxation of emerging excited states reflects the path of an electron in a substance and can be recorded by a camera. Examples of photographs reflecting the results of luminescence observation upon irradiation of polystyrene with a focused electron beam with energies from 10 keV to 80keV are shown in Fig. 2. 1.1.

In the early 1970s, Brewer G.R.[22], and a year later, a group of scientists with the participation of Everhart T. E. [23], used electronic resists to observe the interaction region . An electron resist, such as polymethyl methacrylate (PMMA), is characterized by a change in solubility depending on the dose of electron irradiation. Chemical etching of PMMA after exposure to a focused electron beam leads to the appearance of a cavity in the resist layer. The results of etching (Fig.1.2) are presented by a series of PMMA profile images with the same exposure time by an electron beam with an initial energy of 20keV, but different etchant exposure times. Using the well-known property of the resist, which consists in the fact that those areas that are most exposed to electrons

dissolve the fastest, the dependence of the shape of the cross section of the interaction volume on the value of the current density was obtained.

Fig. 1.2 — Cross-section images of etched PMMA after electron irradiation with a beam with an initial energy of 20 keV at various exposure doses [23]

Images corresponding to the initial stages of etching (Fig.1.2a — c) are cylindrical cavities located directly below the point of incidence of the electron beam. However, with an increase in the etching time (Fig.1.2 d — f), the PMMA regions that are less damaged by electrons are involved in the process, which leads not only to an increase, but also to a change in the shape of the interaction region up to a pear-shaped one (Fig. 1.2 g). The spot diameter of the focused electron beam in the experiment was about and the resulting dimensions of the interaction region in each of the directions are several micrometers.

Further development of ideas about the interaction region is associated with the development of computer simulation of electron scattering by the Monte Carlo method. The next chapter of this work is devoted to discussing the possibilities of using this research method.

1.1.2 Penetration of an electron beam into a solid body

The propagation of electrons in a solid is an important problem from the point of view of methods for analyzing internal properties. The study of the penetration and propagation of an electron beam is an extremely important task. From the point of view of the practical use of electron microscopy, the assessment of the actual resolution of methods for analyzing both surface and internal properties of a sample is based on the shape of the interaction volume formed during the propagation of an electron beam.

The size and shape of the interaction region are determined by the behavior of the electron beam when it enters the subsurface layers of matter. The nature of the motion of accelerated electrons inside a solid body changes as the penetration depth increases. When passing through matter, an electron undergoes many scattering events, which deviate it from its initial direction, and also lead to energy losses. Multiple electron collisions change the nature of the electron beam propagation in the sample. The number of elastic scattering events is a convenient characteristic for designating the boundaries of the stages of electron propagation in a sample. Three main stages can be distinguished, successively replacing each other as the depth of electron penetration increases. The initial stage of plural scattering is replaced by multiple scattering after 20 — 30 collisions. According to the theory proposed by Bothe W in 1929 [24], in the multiple scattering regime, the angular distribution of electrons passing through a layer of matter is described by a two-dimensional Gaussian function. In this case, the part of the beam scattered per unit solid angle in the 6 direction is given by the equation

where I0 is the primary beam current, I(6) is the current collected in the solid angle dQ. Integrating the equation (1.1) over the deflection angle, we obtain the fraction of electrons collected inside the cone with the 6 solution centered at the beam incidence point

where 2\\ is the rms scattering angle for the Gaussian distribution, and Xb is the most probable deflection angle. There are several approximations for describing the depen-

(1.1)

dence of Xb on the layer thickness, which more or less exactly correspond to the experimental data obtained by Cosslett V. E. and Thomas R. N. in 1964 [25]. An example is the expression proposed by Bothe:

An = ^ ^ 1010,

,EoJ A

where the unit of E0 is eV, and Xb is rad, the atomic weight A is expressed in a.m.u., the density is p to cm, and the thickness of x to cm.

The fraction of electrons r] d passing through a layer of thickness x under multiple scattering conditions obeys the well-known Lambert law:

r]D = exp(—pBx), (1.2)

where the absorption coefficient ps is expressed in terms of the most probable deflection angle Xb as

"=° t=2-0 Ai1011

The linearity of the dependence log t]d (x) can be taken as a criterion for the formation of the multiple scattering regime. On Fig. 1.3 reflects the behavior of the transmittance versus the mass thickness of the scattering layer for gold, obtained experimentally by Cosslett and Thomas [26]. The beginning of the linear section is indicated by the dotted line MS.

Starting from a certain thickness of the scattering layer, the behavior of log t]d ((x) ceases to obey a linear law. corresponds to electron diffusion The number of collisions required to achieve it varies from 50 — 60 for heavy elements ( Au, Pt) to 80 — 90 for light ones ( A I, Cu). electron beam obeys the laws of electron diffusion, called the depth of total diffusion. Using Bethe's continuous deceleration model to account for energy losses, in 1961 Archard [27] proposed a theory called the diffusion model. According to this model, electrons can move in any direction from the point of complete diffusion at a depth of Xd in such a way that the total path length of each of them is equal to the mean path length R (Fig. 1.4). The sector of the circle intersecting with the surface of the sample corresponds to the escape of backscattered electrons.

The key quantity for the electron diffusion model is the total diffusion depth. At this depth, according to Bothe's theory, the most probable deflection angle of an electron reaches its maximum value. Bothe's definition of the start of diffusion is that the

Fig. 1.3 — Dependence of the logarithm of the transmittance on the mass thickness of the gold layer. The dotted line MS corresponds to the establishment of the multiple scattering regime, the dotted line D - to the electron diffusion regime [26]

transmittance is 1/e. Later studies by scientific groups led by Cosslett V.E. (1964) [25] and Kanaya K. (1972) [28] showed that the results of calculations obtained according to Bothe's theories differ quite strongly from the experimental data of measurements of the electron scattering parameters. In this regard, another method was first proposed for determining the depth of total diffusion. It is based on the observation that the direction of electron movement is independent of the initial direction of their movement. The it = 0.5 criterion following from this observation reflects the fact that half of the electrons move up and the other half move down. Kanaya K., in turn, modified the electron diffusion model. The use of the model modified by him made it possible to obtain results that were in better agreement with the results of experimental studies and Cosslett's calculations. This model is similar to the Archard model, but the depth of

PE

ir

Fig. 1.4 — Scheme of accelerated electron beam propagation in matter (Archard

model) [27]

total diffusion is replaced by the depth of the greatest energy loss. The picture of the distribution of electrons in the sample, obtained using the Kanaya model, also agrees better with the experimental images of the electron cloud and the electron resist after irradiation.

One of the most significant quantities that determine electron scattering in a substance is the penetration depth of the electron beam. Estimation of this depth is an important task, in particular, related to the determination of the resolution of methods for deep analysis of solids.

The approach used in 1972 by a group of Japanese scientists led by Kanaya to calculate the penetration depth of electrons [28] is related to the study of energy absorption when moving along the normal to the surface. It allows one to estimate the maximum penetration depth of electrons into the sample, as well as the exit depth of backscattered electrons, which is of interest for this work.

Experimental studies of scattering make it possible to relate the depth of penetration of primary electrons into the sample Rz with their energy E:

pRz = CEn. (1.3)

where p is the density of the material, the coefficient C is a value weakly dependent on the atomic number Z, and the exponent n is in the range 1.3... 1.7.

Numerous approximations used in scattering theory make it difficult to compare quantitatively the results of calculation and measurement of Rz . Kanaya K. and Okayama S suggested abandoning attempts at rigorous calculation of certain parameters and replacing them with the selection of some average fitting coefficients that ensure optimal agreement between experimental and theoretical curves in a wide range of E and Z values. In the voltage range of interest to us up to 30keV, the approximate formula describing the electron penetration depth has the form:

27.6A 5

Rz = --irE-5, (1.4)

pZ 9

where A is the atomic weight of the material; Rz is measured in nm, p is measured in

7^3, and E is measured in keV. cm3'

This method of calculating the Rz depth is convenient because it allows one to reduce the individual features of electron scattering on atoms and compounds of various elements to a universal dependence that includes only the parameters p, Z, A. In this regard, the formula (1.4) is widely used in modeling electron scattering in solid samples.

1.1.3 Electron backscattering (BSE) and secondary electron emission (SE)

The impossibility of directly studying subsurface scattering processes in solid samples forces the experimenter to resort to the analysis of secondary products of electron scattering. Information about the internal properties of a sample can be carried by backscattered electrons (BSE) and x-ray photons. The main advantage of the BSE is the smaller amount of interaction compared to X-rays. This provides potentially higher lateral resolution as well as depth resolution.

Experimental and theoretical studies of the BSEs of interest to this work were carried out by many authors [29-33]. The most traditional experimental method for studying backscattering is the observation of the reflection and transmission of a focused electron beam through thin conducting films. This method was used, for example, in the works of Bishop H. and Heinrich K.F.J. in the middle of 1960 — s. Various forms of detection of the obtained scattered, absorbed, and transmitted currents make it possible to speak about the influence of the chemical composition of the sample under study and the parameters of the primary beam on the scattering results.

Fig. 1.5 — Dependence of the electron backscattering coefficient on the target atomic

number Z [34; 35]

The experiments of Bishop and Hendrich mentioned above, comparing the total beam current with the BSE current, make it possible to trace the dependence of the backscattering coefficient on the atomic number. As the latter increases, the value of the coefficient increases monotonically, as can be seen from Fig. 1.5. This dependence is characterized by a strong initial growth, which weakens as the nuclear charge, Z, increases. In the region Z > 50 the corresponding curve becomes gentle. To explain the shape of this dependence, one can resort to the classical concepts of the electron

elastic scattering cross section. The growth of the latter with an increase in Z causes the observed dependence. The curve shown in Fig. 1.5, was approximated by Reuter H. by the following expression:

r] = —0.0254 + 0.016Z — 1.86 • 10—4Z2 + 8.3 • 10—7Z3, (1.5)

which is successfully used in modeling scattering in samples of various elemental composition [36]. Separately, it should be noted that the behavior of the backscattering coefficient satisfies the general dependence represented by the equation (1.5) in the case when the sample is a mixture of elements that is homogeneous on an atomic scale, for example, a solid solution. In this case, the BSE yield can be calculated in accordance with the weight (mass) concentrations of elements:

1 = ^ C%T]%

where i corresponds to the number of the solid solution element, and r/i is the BSE yield of the pure i-th element. Mass concentration is calculated by the formula

a-iAi

Ci =

Xw aiAi

where Ai denotes the atomic weight, and ai is the valence in the chemical compound for the i-th element of the [37] mixture.

The influence of the atomic number on the intensity of scattering underlies the formation of the contrast of materials in the study by means of electron microscopy.

From Fig. 1.5 It is clearly seen that the BSE coefficient in the medium-energy region weakly depends on the beam energy, since the difference between the values of the BSE coefficient in the range of accelerating voltages of the electron beam 5 — 50 keV, which is typical for SEM, is less than 10%. On a qualitative level, this can be explained by the fact that the average penetration depth of electrons increases with increasing energy, while the average value of specific energy losses along the path traveled decreases. At a depth that corresponds to the cessation of motion of an average statistical electron with an initial energy of 10keV, an electron with an energy of 20keV will lose only half of its initial energy. Therefore, it has the ability to change the direction of movement quite strongly and exit through the surface. Thus, there is some compensation for the

increase in the free path with energy, and the BSE yield is practically insensitive to the energy of the incident beam.

A separate experimental task is to record the energy and angular distribution of the BSE current. Its solution requires special experimental equipment and cannot be carried out in serial SEMs.

In addition to the BSE flux, electrons produced as a result of the ionization of atomic shells of the surface layers also escape through the sample surface. These electrons are called secondary (SE) and have a relatively low energy (on the order of a few eV).

There is a fraction of the WEM that has lost most of its energy as a result of scattering. It is practically impossible to separate such low-energy BSE from SE, therefore it is customary to call SE all electrons with energies less than 50 eV, and BSE from 50 eV and higher.

By analogy with the BSE yield, you can enter the coefficient of secondary electron emission (SEE)

Use isE ,, ^

0 = - = —, (1.6)

nB %B

where use is the number of SEs that left the sample, ns is the number of primary electrons. Similarly, for the notation in the representation of currents isE and is - the current of SE that left the sample and the current of the primary beam, respectively.

Understanding the principles of the formation of the SE current and the main dependences of its behavior is extremely important for modern electron microscopy in general and for applications related to lithography, as well as induced deposition of interest to us.

The value of the coefficient of secondary electron emission decreases with increasing energy of the primary beam. This behavior can be explained in terms of the depth of penetration of primary electrons into the sample. The escape depth of secondary electrons is small (on the order of a few nanometers), so SEs generated at greater depths do not leave the sample. However, a decrease in the initial energy of the incident electrons leads to the fact that their penetration depth becomes ever shorter. Because of this, an increasing part of the secondary electrons is born near the surface and has the opportunity to leave the sample. A further decrease in energy leads to an even greater increase in the SEE coefficient to unity and higher. The [38] authors proposed a univer-

sal relation relating the energy of an electron to its mean inelastic free path in matter. The form of this dependence is shown in Fig. 1.6.

Electron energy,

Fig. 1.6 — Dependence of the energy of an electron to its mean inelastic free path in

matter [38]

The vast majority of SE is produced as a result of interaction between high-energy primary electrons and conduction electrons in metals or electrons of outer atomic shells in semiconductors and insulators. The SE energy distribution is concentrated in a narrow region and has a peak in the 2 — 5eV region. The choice of the upper energy limit of 50eV is connected with the historical tradition. At the same time, more than 90% secondary electrons have energies less than 10eV.

The main consequence of the low SE energy is a relatively small (less than 50 nm) exit depth. SE generation occurs along the entire trajectory of the primary beam inside the sample. However, one should not forget that SEs are also subject to inelastic scattering and concomitant energy losses in the process of passing through the sample. It is also worth noting that when an electron reaches the surface, it must overcome a potential barrier corresponding to the work function of the electron. This requires a kinetic energy of several electron volts. Since the SE current is greatly attenuated due to inelastic scattering, the yield probability decreases exponentially with depth:

p & exp

(1.7)

where p is the exit probability, z is the depth of occurrence of the SE, and A is the mean free path of the SE. In 1983, Seiler H. [39] estimated the maximum depth of SE to be 5A, and the value of A is about 1nm for metals and above 10nm for insulators. The significantly longer mean free path in insulators is explained by the fact that the inelastic scattering of SE occurs primarily on conduction electrons, the number of which in conductors is large, while in insulators it is quite small.

Among SEs generated during the scattering of the primary beam, two types of electrons can be distinguished: SE1 and SE2. The primary beam generates visible (emerging through the surface) SEs in the process of moving deep into the sample up to 5A of the exit depth from the surface. Such electrons are called SE1, emphasizing their connection with primary electrons. The electron current SE1 is usually strongly localized near the beam incidence region. At the same time, the primary electron repeatedly scattered inside the sample, which emerged through the surface as a backscattered electron, also generates secondary electrons. SEs that appeared at a depth less than 5A from the surface have the opportunity to exit through the surface. These electrons are designated SE2. Since SE2 are in fact the result of backscattering, their characteristic as a useful signal is determined by changes in the distribution of the BSE.

For low primary beam energies E0 < 5keV, the penetration depth of primary electrons and the BSE exit depth decrease so much that the exit depth SE ceases to depend on the primary beam energy.

The total SEE coefficient St consists of two components 61 and S2 corresponding to SEi and SE2:

5T = 5i + rjS2, (1.8)

where the coefficients S1y2 represent the contribution per electron of the primary beam. The values 61 and S2 are not equal. This indicates the different efficiency of SE generation by the primary beam electron and the average BSE. Usually the ratio — is about

o2

3 — 4. Accordingly, BSEs generate SEs much more efficiently than the same electrons when they only enter the sample as primary ones. This behavior is explained by the existence of two main factors. First, the effect of multiple elastic collisions leads to the fact that a significant part of the BSE moves towards the surface at an angle less than normal. Thus, the length of the path in the 5A layer will be larger. The additional path length in comparison with a normally incident primary electron leads to the generation of a larger number of SEs that have left the sample. Second, the inelastic scattering of

an electron in the process of moving through the sample causes energy losses. As a result, the BSE has a lower energy than the primary electron. In this regard, the cross section of the BSE collision is larger and, accordingly, the efficiency of energy transfer to weakly bound electrons of the substance is higher.

In contrast to the BSE coefficient, which changes monotonically with atomic number, the WEE coefficient is almost insensitive to the composition of the sample. For the vast majority of elements, the value of the SEE coefficient at a fixed value of the primary beam energy does not change, for example, for 20keV, the SEE coefficient is 0.1. The exceptions are carbon and gold, for which this value is 0.05 and 0.2, respectively. However, it should be noted that the process of secondary electron emission is extremely sensitive to the state of the surface under study. For example, in serial SEM, the chamber of which is not cleaned using special techniques, during the study of the sample, a layer of carbon contamination is formed on its surface, which affects the SEE.

When studying the flow of electrons through the surface without additional energy filtering, both BSE and SE are registered. In order to relate information about the internal properties of the sample and the properties of the electron flow, let us consider the processes accompanying the penetration of an electron beam into a solid.

1.2 Methods of layer-by-layer analysis of samples

In the modern science-intensive industry aimed at the production and use of microelectronics, a special place is occupied by multilayer structures. In this regard, the development of methods for analyzing the composition of multilayer samples is an important and urgent task. The most common tool for monitoring the morphology and composition of conductive samples is SEM.

The simplest and clearest way to control the composition of a multilayer sample is by sputtering or creating a cross section using a sharply focused ion beam. Material sputtering techniques are characterized by the joint use of tools for direct sample etching and methods for analyzing the chemical composition of the surface or the flow of secondary ions formed during sputtering.

One of the simplest and most accurate methods for studying the composition of a layered sample is to observe its cleavage [40]. The shearing, as a rule, is carried out

along the crystallographic plane, which leads to the appearance of a smooth side surface. The study of the obtained surface makes it possible to obtain information about the depth of the layers, as well as their inhomogeneity in thickness along the cleavage for different spatial sections of the sample. This research technique is excellent for single crystals, however, for materials with malleability, primarily metals, it is quite difficult to obtain a chip. This circumstance significantly limits the applicability of this method.

Much more versatile than the cleavage technique are methods based on sample spraying. One of the common methods is the combined use of sample sputtering with an accelerated flow of argon ions and registration of Auger electron spectra, described in [41]. Slow (less than 1 nm/min) sputtering with argon after calibration makes it possible to very accurately trace the layer-by-layer structure of the sample, and the Auger electron spectrum of the surface makes it possible to control the chemical composition during sputtering. The lateral resolution of this method is limited by the spot size of the focused electron beam in OES, which reaches 1 ^m. An additional difficulty for the widespread use of this technique for monitoring the composition of a sample is the condition of ultrahigh vacuum, which is necessary for recording the Auger electron spectrum.

A much higher lateral resolution (tens of nanometers) has a method of forming a cross section using a focused ion beam. The use of instruments equipped with crossed beams makes it possible to control the cut by means of electron microscopy without changing the position of the sample. This makes it possible to reduce the exploration time and avoid the accumulation of errors associated with positioning. An undoubted advantage over the method of layer-by-layer recording of OES is the possibility of selecting small areas for forming a cross section and subsequent analysis of the internal structure of the sample in this area. The requirements for the vacuum part are also significantly lower and correspond to the operating conditions of serial SEMs. The main disadvantage of the method is the great difficulty in forming a vertical cut plane. The accompanying lateral etching of the sample, along with etching in depth, distorts the result of measuring the thicknesses of the elements of the structure under study on the cut. The distortion increases with increasing etch depth. In addition, electron microscopy only makes it possible to determine the boundaries of the layers, but additional equipment is required to determine their chemical composition.

An alternative method, also widely used in the field of monitoring the composition of complex samples, is the method of mass spectrometry of secondary ions. The analysis of the structure by this method is based on the registration of the change in the

mass spectrum during the sputtering of the sample. A key challenge for precision measurements is the need to calibrate on reference samples due to the different etch rates for different materials. It is also necessary to take into account the effect of ion implantation and layer mixing during etching.

All of the above methods provide a potential opportunity to determine the structure of a sample of any complexity and thickness. However, each of them leads to the destruction of the test sample. In this regard, the issue of non-destructive analysis methods, which we will discuss below, becomes topical.

1.2.1 Analysis of sample structure using X-rays

The inelastic interaction of beam electrons with the sample under study leads to the appearance, among other things, of characteristic X-ray radiation. The analysis of this radiation makes it possible to obtain not only qualitative information about the presence of certain chemical elements in the composition of the sample, but also to determine their quantitative ratio in the study area. Energy-dispersive analysis of X-ray radiation is the most widely used technique used to study the chemical composition of samples in electron microscopes. The essence of the technique is as follows. When a characteristic X-ray photon is absorbed by a semiconductor diode (for example, based on silicon doped with lithium), a photoelectron is knocked out. The energy of this pho-toelectron is spent on the generation of electron-hole pairs, which are stretched by an external electric field and form a pulsed discharge. The magnitude of this discharge is proportional to the energy of the ejected photoelectron and, accordingly, to the frequency of the absorbed primary photon.

An important part of the technique is the ability to quantify the content of various chemical elements. There is a generally accepted system of corrections (ZAF — correction) that makes it possible to calculate the actual values of concentrations from experimental data on the ratios of the signals of different elements. The said recalculation of the number of characteristic photons to determine the abundance of an element is determined by the product of three correction factors. The atomic number correction factor Z takes into account the change in the intensity of the characteristic X-ray radiation depending on the atomic number. This change is connected, on the one hand, with

the influence of Z on the scattering properties of the substance, which determine the WSE coefficient; on the other hand, on the density of electronic states in the material. The use of the absorption correction factor A is due to the fact that the characteristic photon can be absorbed by the atoms of matter, primarily due to the photoelectric effect. The probability of photon absorption depends on the chemical composition of the sample, as well as the depth of its occurrence. Compensation for secondary fluorescence caused by the absorption of a primary characteristic photon by an atom of another element, followed by the emission of X-rays of lower energy, is carried out using the fluorescence correction factor F. Thus, the use of the ZAF correction system makes it possible to recalculate the fractional content of chemical elements in a multicomponent material. One of the most interesting examples of such a multicomponent material is multilayer structures.

There are several works devoted to the study of the subsurface structure of multilayer samples using X-ray dispersion analysis [42-46]. Despite significant differences in the details concerning the computational part of solving the problem of the thickness of layers in a sample, it is possible to single out a sequence of actions common to most authors.

1. Observation of the characteristic X-ray spectrum of the studied multilayer samples and corresponding standards with accompanying correction using the ZAF system or using commercial software, such as OxfordlNCA.

2. Plotting curves for the dependence of the proportion of the element of interest in the structure under study on the energy of the primary electron beam.

3. Building a model of the interaction of a sample with a primary electron beam to calculate the depth of exit of the characteristic radiation with subsequent calculation of the layer thickness in the sample. Various methods are used to theoretically describe the features of X-ray study generation in multilayer samples: Monte Carlo simulation [46; 47], using the Pouchou and Pichua procedure (Pouchou J. — L, Pichoir F.(PAP)) [43], plotting the sample effective density curve [44].

On Fig. 1.7 illustrates the principle of calculating the unknown thickness of the gold layer on silicon [47].

The high accuracy (from 2% to 10%, indicated by different authors for various systems under study) and the wide availability of the corresponding detectors in modern SEMs make the technique for determining the layer thicknesses in multilayer samples

Fig. 1.7 — Dependence of the intensity of the detected X-ray radiation on the energy

of the primary electron beam [47]

using X-ray dispersion analysis very promising. However, it has a number of disadvantages, including difficulties in the study of light (Z < 11) elements, associated with the complexity or fundamental impossibility of detecting the characteristic radiation of the corresponding elements. First of all, when X-ray photons are observed for light elements, their strong absorption in the sample itself is manifested. The chemical environment of the atoms of the substance under study affects the position of the registered spectral lines, which also negatively affects the detected signal. Another difficulty is the need for reference samples with known composition and morphology. Such standard samples are expensive and not always available to the experimenter, which can significantly limit the range of materials available for research.

1.2.2 Methods for analyzing multilayer samples using scattered electrons

The detection of X-ray photons is in itself a rather nontrivial task. Unlike photons, electrons are charged particles, which greatly facilitates the process of collecting and processing the corresponding signal. In this regard, there are many methods of analysis based on the detection of electrons, both secondary and backscattered.

Energy selection of secondary electrons

The processes associated with the excitation and ionization of atoms of a substance form a stream of secondary electrons. The energy distribution of these electrons carries information about the structure of the energy levels of the substance under study. Analysis techniques such as X-ray photoelectron spectroscopy (XPS) and Auger electron spectroscopy include registration of the electron energy distribution and are successfully used to determine the thickness of surface layers.

X-ray photoelectron spectroscopy (XPS) , which is based on the use of the photoelectric effect, is associated with the action of an X-ray photon beam on a sample. The photoelectrons that appear as a result of this action reflect the features of the energy structure of the substance under study, associated both with the chemical composition and with the chemical environment. The XPS method is often used to determine the thickness of thin surface films [48]. For this, information is used on the ratio of the intensities of the peaks of the layer material and the substrate, expressed by the equation:

where dsl is the film thickness, Isl and In are the intensity of the photoelectron peak for the layer and substrate, respectively, À is the mean free path of a photoelectron in the layer material, 6 is the angle between the sample surface and the direction of incidence of the probing beam, and fi = ^/jf /^f ) is the ratio of the heights of the substrate and material peaks corresponding to massive samples.

The accuracy of measuring the thickness of the surface layer, achieved by modern research groups in the range of measured thicknesses up to 2nm, is 0.1nm [49; 50]. The same research groups note that determining the thickness of the surface layer in the range above 10nm presents big problems. The upper limit of the layer thickness that can be analyzed by XPES is 30nm, which corresponds to the maximum depth of photoelectron escape.

Auger electron spectroscopy The OES mentioned earlier can also be used to analyze multilayer samples [51]. In contrast to XPS, when registering the Auger electron spectrum, irradiation is performed with a beam of accelerated electrons. Non-destructive analysis of the sample structure is carried out by comparing the intensity of the Auger electron peaks. The key observation here is the exponential decay of the substrate signal with increasing thickness of the surface layer. The equation relating the intensity of the Auger electron peak for a substrate I covered with a layer of material x thick, with the corresponding intensity for a clean substrate I0, has the form:

I = Io exp (—x/X), (1.10)

where A is the mean path of an Auger electron in the substrate material. A similar equation for the intensity of the Auger electron peak for the layer material has the form:

7sl = Is\,o exp (—^/Asl) ' (L11)

where the index "sl" indicates the corresponding parameters for the layer material. The calculation of the layer thickness, in this case, is based on the ratio of the peak heights of the layer and the substrate. At present, the use of OES makes it possible to measure the thickness of layers in the subnanometer range [52; 53]. However, the applicability of the method is limited only to ultrathin films (0.1 — 10nm). This is due to the small mean free path of the Auger electron, which is included in the equations for the peak intensity (1.10, 1.11).

Thus, we can conclude that methods for analyzing multilayer samples based on the energy filtration of secondary electrons (photoelectrons and Auger electrons) are of exceptional interest for studying ultrathin films. At the same time, the upper limit of the film thickness, which limits the application of these techniques, does not allow one to study the deep structure of the samples, the analysis of which is the goal of this work.

The basis for a whole series of different methods of nondestructive analysis of multilayer structures in SEM is the use of backscattered electrons. The information depth of the WSE can reach several microns, which is significantly greater than the depth of the exit of secondary electrons, as mentioned above. At the same time, the amount of interaction corresponding to the recorded BSE signal is significantly less than for the characteristic X-ray radiation produced by the same PE beam. This makes it possible to expect better spatial resolution in the analysis of multilayer samples using techniques based on the study of the WSE.

Investigation of the change in the WSE current

The simplest and most obvious approach to studying the subsurface structure of a sample using the BSE is to measure the BSE current. Let's consider this approach in more detail on the example of the methodology proposed by the scientific group led by Haimovich J. [54; 55].

The method is based on the use of the concept of information depth. The primary beam electron travels some distance inside the sample before returning to the surface as a BSE. It carries information about the sample within certain depth limits. This limit is called the information depth. If the information depth is less than the thickness of the deposited layer, backscattering will occur only in this layer. The BSE coefficient in this case will correspond to the BSE of the layer material In the opposite situation, when the thickness of the deposited layer is much less than the information depth, the primary beam will be scattered only in the substrate. In this case, the FOS of the structure is determined by the FOS of the substrate material For comparable values of the information depth and layer thickness, the CSE of the sample takes on an intermediate value ^t, which lies between ^ and r¡n .

To determine the thickness of a thin layer, it is necessary to know how the CODE changes with a change in the layer thickness t for a given layer-substrate pair of materials. This dependence can be determined experimentally by creating a series of model samples with a known structure and then measuring the RSE for each of them. To predict the results of the experimental study, the simulation of electron scattering by the Monte Carlo method was used. The chosen model involves using the traditional ap-

proach described by Joy D.C. [56]. The electron elastic scattering cross section within this model is calculated using the Rutherford formula for the case of a screened nucleus (3.3). The Bethe formula (3.1.2) is used to take into account energy losses during the passage of an electron through matter.

Based on the results of modeling for various initial conditions, the desired curve of the dependence of the CSE on the layer thickness was constructed. The figure 1.8 illustrates the curves for different initial electron energies.

Layer mass-thickness, jig tm-2 Layer mass-thickness, jig cm-2

Fig. 1.8 — Curves of the dependence of the electron backscattering coefficient on the thickness of the surface layer for the layer-substrate structure for a nickel-gold pair at different initial electron energies (a) - 5 keV, (b) - 10 keV , (c) - 15 keV, (d) - 20 keV

[54]

The solution of the inverse problem of finding the layer thickness from the known value of the BSE current was carried out analytically, based on the approximation of the obtained dependence.

Experimental study of energy spectra of the BSE

One of the approaches to the tomography of multilayer structures using the BSE is the analysis of their energy spectra. In order to use the energy characteristics of the WSE to predict the structure of multilayer samples, a group of scientists led by Rau E.I. it was proposed to create an electrostatic toroidal spectrometer (ETS) [29; 57-59]. The corresponding method of layer-by-layer analysis is based on the dependence of the maximum electron range in the substance R0 on the initial energy. To calculate Ro, the [60] authors used the Thomson-Widdington law and the semi-empirical formula obtained by Kanaya K. and Okayama S., in the form:

E0 — El = CY, (1.12)

where E0 is the initial energy of the electron, E\ is the energy of the electron after passing the path Y, C is a constant depending on the atomic number Z, the atomic mass A and the density of the sample material p. The exponent n takes the value 2 for the Thomson-Widdington law or 1.67 for the Kanaya-Okayama formula (Kanaya — Okayama).

To correlate the path length with the depth of the layer, a peak is searched for in the energy spectrum of the WSE. It is assumed that electron backscattering occurs at a large angle 9 with respect to the normal to the surface by means of unit scattering at depth X. In this case, the total length of the path Y can be written as Y = X + . Accordingly, the energy of the WSE scattered through the angle 9 correlates with the desired depth X by the expression:

cos 9

-. (1.13)

X

R0 1 + cos 9

On Fig. 1.9 shows the spectra experimentally obtained using the ETS [60]. The plotted curves reflect the distribution of the BSE for massive aluminum (Al) and copper (Cu) substrates, as well as for two-layer structures of the layer-substrate type based on aluminum and copper. In addition to the experimental curves, the figure also shows the results of modeling the response of layered samples obtained by the Monte Carlo method. The model used is based on the representation of the elastic scattering cross

section in the form proposed by Mott N.F.(3.4), and the energy losses were calculated using the Bethe formula:

13

E, keV

Fig. 1.9 — WSE energy spectra from bulk and multilayer samples: 1 - bulk aluminum (Al), 2 - bulk copper (Cu), 3 - 800nm Al on Cu substrate, 4 - 400nm Al on Cu substrate, 3' — 4' - corresponding spectra obtained by Monte Carlo simulation [60]

There is another method for determining the thickness of thin films on massive substrates using the energy spectra of the BSE, proposed by a group of scientists led by Zhenyu T. [61]. The applied algorithm is based on the analysis of the general structure of the energy spectrum of the WSE and involves the joint use of experimental data and Monte Carlo simulation results.

The above non-destructive analysis techniques are based on the registration of the total intensity of the detected signal. As noted above, there is a distribution of the electron density over the volume of the interaction region. A change in the PE current obviously leads to a change in the relative contribution from different parts of the interaction volume to the resulting signal. The mentioned methods of research do not reflect this circumstance. In this paper, we consider a significantly different approach to studying the results of scattering of a beam of primary electrons, based on the spatial distribution of the BSE flux. The study of the distribution of the surface current density

of the BSE is naturally related to the distribution of electrons in the interaction volume; therefore, the proposed approach opens up new possibilities for studying the internal structure of samples irradiated by a focused electron beam.

In subsequent chapters, an overview of the used sample preparation and experimental analysis techniques will be given (Chapter 2), as well as a theoretical description of the processes underlying the technique for recording surface current density, and the possibilities of modeling these processes will be considered (Chapter 3). In the final chapter (Chapter 4), the results of Monte Carlo simulations of electron scattering for real systems will be presented in comparison with the data of corresponding experimental studies.

Chapter 2. Experimental methods

In the previous chapter, we briefly discussed the theoretical foundations and fundamental possibilities of studying the internal structure of solids in an electron microscope. Several methods for analyzing the subsurface composition of samples are also considered. The implementation of the method of layer-by-layer research proposed in this paper is impossible without practical experimental studies with careful control of the exposure conditions and the possibility of verifying the results obtained by independent methods. This chapter contains descriptions of the experimental setups and methods directly used in conducting experiments and verifying the reliability of their results, as well as in preparing model samples.